What is the answer to |4-x|=|2x+1| ?

The answer to |4-x|=|2x+1| is x=-5\lor x=1

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|4-x|=|2x+1|

∣ 4 - x ∣ = ∣ 2 x + 1 ∣

x = - 5 or x = 1

Solution steps

∣ 4 - x ∣ = ∣ 2 x + 1 ∣

Find positive and negative intervals

x < - \frac{1}{2}, - \frac{1}{2} \leq x \leq 4, x > 4

Solve the inequality for each interval

x = - 5 or x = 1 or No Solution

x = - 5 or x = 1

x^{2} + 21 x - 20 \geq 4 x - 80

4 x^{2} = 4 x

105 n^{3} + 175 n^{2} - 75 n - 125

x^{2} + 1 = 5 x

\frac{2}{3} + \frac{3 k}{4} = \frac{71}{12}